Cyclic codes over a linear companion of Z/sub 4/

We introduce linear cyclic codes over the ring R=F/sub 2/+uF/sub 2/={0,1,u,u~=u+1}, where u/sup 2/=0. This ring shares many properties of Z/sub 4/ and F/sub 4/ and admits a linear "Gray map". Self-dual cyclic codes of odd length exists as in the case of Z/sub 4/-codes. We give a BCH-like bound for these codes and describe a simple algebraic decoding procedure.